Functional Matching and Renormalization Group Equations at Two-Loop Order

Abstract

We present a systematic method for determining the two-loop effective Lagrangian resulting from integrating out a set of heavy particles in an ultraviolet scalar theory. We prove that the matching coefficients are entirely determined from the (double-)hard region of the loop integrals and present a master formula for matching, applicable to both diagrammatic and functional approaches. We further employ functional methods to determine compact expressions for the effective Lagrangian that do not rely on any previous knowledge of its structure or symmetries. The same methods are also applicable to the computation of renormalization group equations. We demonstrate the application of the functional approach by computing the two-loop matching coefficients and renormalization group equations in a scalar toy model.

13 pages, 2 figures. v2: Matching journal version

References in corpus (13)

• Integrating out heavy particles with functional methods: a simplified framework
• A Proof of Concept for Matchete: An Automated Tool for Matching Effective Theories
• Extending the Universal One-Loop Effective Action: Heavy-Light Coefficients
• The Fermionic Universal One-Loop Effective Action
• STrEAMlining EFT Matching
• Evanescent Operators in One-Loop Matching Computations
• Integrating Out New Fermions at One Loop
• Third-Family Quark-Lepton Unification and Electroweak Precision Tests
• Landscaping CP-violating BSM scenarios
• Renormalization and non-renormalization of scalar EFTs at higher orders
• Simple Rules for Evanescent Operators in One-Loop Basis Transformations
• Dipole operators in Fierz identities
• New Covariant Feynman Rules for Effective Field Theories

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